This Cross Multiplication Calculator, provided by Hesapstan, solves one missing value in a proportion of the form a/b = c/d or checks a filled proportion by comparing the two cross products.
What does this cross multiplication calculator do?
The calculator works with proportions written as a/b = c/d. If exactly one field is left blank, it solves the missing value. If all four fields are filled, it checks whether the proportion is true.
- One blank field starts solve mode.
- Four filled fields start verify mode.
- The solution shows the original proportion, cross multiplication, isolation step, and check.
- The denominator fields b and d cannot be 0.
The main purpose of this page is to show the cross-multiplication method step by step. A broader ratio and proportion calculator may solve similar problems, but this tool is focused on the a/b = c/d setup and the cross-products behind it.
What is cross multiplication?
Cross multiplication compares or solves a proportion by multiplying each numerator by the opposite denominator. In a/b = c/d, the cross multiplication equation is a × d = b × c.
For example, in 3/4 = 6/d, the cross products give 3 × d = 4 × 6. This equation can then be solved for d.
What do a, b, c, and d mean?
The calculator keeps the formula variables as a, b, c, and d so the steps remain readable across languages and match the mathematical notation.
- a: numerator of the first fraction
- b: denominator of the first fraction
- c: numerator of the second fraction
- d: denominator of the second fraction
Because division by 0 is undefined, b and d cannot be 0.
How does solve mode work?
In solve mode, exactly one of the four fields is blank. The calculator writes the proportion, forms the cross-multiplication equation, and isolates the missing value.
Example: for 3/4 = 6/d, cross multiplication gives 3 × d = 4 × 6. Therefore d = 24 / 3 = 8, and the check is 3/4 = 6/8.
This calculator solves one missing field at a time. Two or more blank fields do not produce a normal result.
How does verify mode work?
When all four fields are filled, the calculator checks the proportion instead of solving for a missing value. It compares a × d with b × c.
For 3/4 = 6/8, the two cross products are 3 × 8 = 24 and 4 × 6 = 24. Since they are equal, the proportion is true.
If the cross products are different, the two fractions do not form a true proportion.
Examples
- 3/4 = 6/d → 3 × d = 4 × 6 → d = 24 / 3 = 8.
- a/5 = 12/20 → a × 20 = 5 × 12 → a = 60 / 20 = 3.
- 3/4 = 6/8 → 3 × 8 = 24 and 4 × 6 = 24, so the proportion is true.
- 2/5 = 4/9 → 2 × 9 = 18 and 5 × 4 = 20, so the proportion is false.
How to use the calculator
- Write your proportion in the form a/b = c/d.
- Leave exactly one field blank to solve it, or fill all four fields to verify it.
- Make sure b and d are not 0.
- Read the result, cross multiplication, solution step, and check.
This is useful for classroom proportion problems, scaling, similar triangles, and simple price-quantity relationships. It is not a unit converter or a general equation solver.
Common mistakes
- Leaving two blanks and expecting a single answer.
- Entering 0 in b or d.
- Comparing only numerators or only denominators instead of cross products.
- Expecting solve mode when all four fields are filled.
- Trying to use the calculator for symbolic algebraic expressions.
Limitations
This calculator solves or checks proportions in the form a/b = c/d using cross multiplication. It does not solve systems of proportions, handle more than one unknown, perform symbolic algebra, convert units, or accept denominators equal to 0.
The result is intended for learning and practical calculation. Very large or invalid numeric inputs may not produce a normal result.
Frequently Asked Questions
What is cross multiplication?
In a/b = c/d, cross multiplication means comparing or solving with a × d = b × c.
How do I solve 3/4 = 6/x?
Cross multiplication gives 3 × x = 4 × 6, so x = 24 / 3 = 8.
Can I leave any one field blank?
Yes. Solve mode works when exactly one of a, b, c, or d is blank. Two or more blanks are not enough for a normal result.
What happens if all four fields are filled?
The calculator switches to verify mode and compares a × d with b × c to decide whether the proportion is true.
Why can the denominator not be 0?
A denominator of 0 would mean division by 0, which is undefined. That is why b and d cannot be 0.
Is this different from a ratio calculator?
Yes. This page focuses on cross-multiplication steps. A ratio/proportion calculator may be broader, while this tool is built around a/b = c/d.